対称空間の代数的モデルとしての準群(II)

In the previous paper [3], we introduced a concept of symmetric loop and showed that it is obtained, interchangeably, from a quasigroup of reflection with a base point. The latter is an algebraic model of symmetric space([4],[5]). In this paper, we shall investigate further properties of symmetric loop G about di-associaticity(§1)and show that the left inner mapping group is a subgroup of AutG(§2). In §3, we shall give an embedding of G into a group AutG*, the automorphism group of the quasigroup of reflection of G. The method of embedding was suggested, essentially, by Professor Kiyosi Yamaguti in his recent letter to the author.